> ;: ' \pWilliam Ba==ZxDAD<
double entry!"
double entry!"B
$$$
EF
G
RS
T(
tV
tt!,^8U)zjo@ DDu^8U)zjo@ Du
$$$$$
EF
G
RS
T(
t7
ttA+Pi1(? +?DADDAuPi1(? +?DADDu
f
$$$$$$
$$$$$
E!F
G#
R4S
T"
tU
tt`pF$? XJDD< B$DDdinvalid efficiencyB`vF$? JDD< B$DDdinvalid efficiencyBvf$$$$$$
$$$$$
EF
G
RS
T$f
g
0I
12
`J
.K
`L
/M
E%F
G&
R%S
T'(
)W $$$$$$$
HF
G_
US
T`(
T
:AqF$? D}F$? D~$$$$$$$
HF
G*
US
T+
%3%* s$$$$$$$
IJ
K(
VW
X)( {
TDT3+w_>@ DDDy_>@ Dz$$$$$$$
Y,hhhhi(
^xyz
0S
12>>>>>(""
g>
ja
k<
lb
[c
mmDcld|8DHR<~Pp|Z68 @!@"#?$?%?&?@'?@(?@)?@*?@+?@,?@-?@.?@/?@0?@1?@2?@3?@4?@5?@6?@7?8?9?@:?@;?<@=@>@??@" n"((((
"((# n#((ZZ
#((&$((((((((((((((((%(+,,--./0017(8(
:ZZ
;((Dl***
"
@?@A?@B?@C?@D@E?@F?@G?@H?@N@O@(
6l
A@"``0]`l(#
0<The used above would be the value of the angular speed if the rotor had only one blade. If it has n blades, then the speed of rotation is reduced n times. This is because n blades sweep n times as much area per unit time; therefore, A is swept n times faster.<0I`Z1d6Ui
6
A@"`F
]`h$
<!P is the power in the wind, or the input power to the wind turbine.
Assuming an efficiency of the turbine, the rotor power output, say Pr is: < ,i
6
A@"`vr]``%
<Comment: If there is no opposition to rotation, the rotation will accelerate, theoretically, indefinitely. In reality, there is opposition to rotation; if T < this opposing torque, there is no rotation; when T becomes equal to it, rotation can be sustained <
6\
A@"`T]`\X&
<UFor a given rotor of radius r and efficiency , wind speed and air density combination, the power output of the rotor is fixed. This is equal to r p r2 v3; therefore,<i
6
A@"`l0]`P'
1<2at a constant rate; if T > opposing torque the rotor will accelerate. The opposing torque is made up of two main components: one due to resistive/ frictional forces and one due to the load. Both components may be considered as having a fixed part and a variable part, the latter depending on the speed of rotation.
The angular acceleration (and deceleration) depends on the moment of inertia of the rotor.
There is an analogy with linear motion: mathematically the formulas are the same as those of Newton's Laws of Motion. The analogies are given in Table 1.<1i >
@Kn
7ggD
' S
dMbP?_*+%"??U>@7
Oh+'0HPhx
Phoebus SparosWilliamMicrosoft Excel@ћ\@}@3@N՜.+,04 PXdlt|
'Rotor Torque Calculation SheetSheet3,'Rotor Torque Calculation Sheet'!Print_AreaWorksheets
Named Ranges
!"#$%&'()+,-./013456789Root Entry F;4RWorkbookSSummaryInformation(*DocumentSummaryInformation82